Free Surface Fluctuations Research Articles

Interactions between swell and colinear wind short crested waves, following and opposing

When wind blows over a water surface during a swell, it generates short-crested, three-dimensional waves that interact with the underlying flow field through a mechanism that ultimately increases the average energy. In the present work, two test cases in which wind is flowing following and opposing a swell are analysed with experiments and are compared with wind-wave-only and swell-only cases. The analysis of the free surface fluctuation and of the flow field, with the three components of fluid velocity measured at the same time through a stereo particle image velocimetry system, leads to an accurate quantification of the energy distribution, of the structure of the oscillating, fluctuating (due to wind-waves) and turbulent kinetic energy, without assumptions on the structure of the flow. The findings demonstrate that the transverse dynamics is a pivotal factor in the transfer of energy in the near-free surface domain, and elucidate the energy transfer between wind-waves and swell. The results also confirm the reduction of oscillating kinetic energy of the swell in the presence of short wind-waves, a process interpreted with different possible mechanisms. There is evidence of the enhancement of wind action in the presence of swell compared to that in the case of wind-waves-only, confirming that energy transfer from the wind to the sea is enhanced when wind flows over a swell. Consequently, when the fetch is influenced by swells generated or propagated from different regions, and during multi-peak sea storms, wave generation models should account for this amplification.

Discussion of ‘Air entrainment and free-surface fluctuations in A-type hydraulic jumps with an abrupt drop’ by Maoyi Luo, Hang Wang, Ruidi Bai, Xiaohui Zheng, David Wüthrich and Shanjun Liu

Discussion of ‘Air entrainment and free-surface fluctuations in A-type hydraulic jumps with an abrupt drop’ by Maoyi Luo, Hang Wang, Ruidi Bai, Xiaohui Zheng, David Wüthrich and Shanjun Liu

Three-Dimensional Numerical Simulation of a Two-Phase Supercritical Open Channel Junction Flow

This study investigates the computational fluid dynamics (CFD) modeling of supercritical open channel junction flow using two different turbulence models: k-ω shear stress transport (SST) and k-ω SST scale-adaptive simulation (SAS), in conjunction with Volume of Fluid (VOF) and mixture multiphase models. The efficacy of these models in predicting the intricate free surface fluctuation and free surface elevation in a supercritical junction is evaluated through a comprehensive analysis of time-averaged free surface data obtained from CFD simulations and Light Detection and Ranging (LIDAR) measurements. The dimensionless Reynolds (Re) and Froude (Fr) numbers of the investigated scenario were Fr = 9 and Re = 5.1 × 104 for the main channel, and Fr = 6 and Re = 3.3 × 104 for the side channel. The results of the analysis demonstrated a satisfactory level of agreement with the experimental data. However, certain limitations associated with both CFD and LIDAR were identified. Specifically, the CFD performance was limited by the model’s incapacity to consider small-scale turbulent effects and to model air bubbles smaller than the cell size while the LIDAR measurements were limited by instrument range, inability to provide insight into what is happening below the water surface, and blind spots. Nonetheless, the k-ω SST turbulent model with the VOF multiphase model most closely matched the LIDAR results.

Low-order modelling of three-dimensional surface waves in liquid film flow on a rotating disk

Using low-dimensional numerical simulations, we investigate the characteristics of complex and three-dimensional surface waves in a liquid film flowing over a rotating disk, focusing on large flow rates from a nozzle. Existing integral boundary layer (IBL) models, which are based on spatially averaged variables along the direction normal to the disk surface, have primarily focused on the formation of axisymmetric waves under relatively small flow rates. In this study, an extended IBL model that accounts for both laminar and turbulent regimes is developed by considering the non-uniformity of the local flow rate in the spreading film flow and incorporating closure models dependent on the local Reynolds number. Our numerical results successfully capture the generation of concentric waves by an impinging circular liquid jet and their transition into three-dimensional solitary waves. These findings are in good agreement with visualization images and time-series data of free-surface fluctuations from a displacement sensor. The backscattering of small-scale three-dimensional turbulence into large-scale horizontal turbulence inside the film plays a critical role in determining the transition of wave modes and the nonlinear dynamics of the waves in the turbulent regime. Furthermore, the behaviour of three-dimensional waves in the downstream region, including frequent wave coalescence in the transition region and the breakup of small-scale solitons, is distinct from that of gravity-driven falling film flows. The amplitude of the three-dimensional waves is inversely related to the generalized Reynolds number defined for rotating films.

铅铋池式快堆自由液面波动致气体夹带行为研究

铅铋池式快堆自由液面波动致气体夹带行为研究

Observing Liquid Sloshing Based on a Multi-Degree-of-Freedom Pendulum Model and Free Surface Fluctuation Sensor.

Rollover prevention of partially filled tank trucks is an ongoing challenge in the road transportation industry, with the core challenge being real-time perception and observation of the liquid state inside the tank. In order to realize reliable observation of a sloshing liquid, this article first proposes a sloshing modeling method based on a multi-degree-of-freedom pendulum model and derives the double mass trammel pendulum model (DMTP, 2DOF) accordingly, which accurately reflects the sloshing dynamics under wider operating conditions. Second, a free surface fluctuation sensor is designed based on magnetostriction, capable of measuring the inclination and height of the liquid level inside tanks filled with hazardous chemicals. Finally, the unscented Kalman filter (UKF) is utilized to synthesize the information of the two, establishing a credible real-time observation of the sloshing liquid. Verified using a vehicle-fluid coupled co-simulation, under the condition of a consecutive double lane change, the observation error of the proposed method is only 25.9% of that of the open-loop calculation, providing a secure guarantee for the observation of the state variables of the single pendulum model (SP) used for most kinds of anti-rollover control.

Numerical simulation of fluid flow and free surface fluctuations during wheel and belt casting process

Numerical simulation of fluid flow and free surface fluctuations during wheel and belt casting process

Air entrainment and free-surface fluctuations in A-type hydraulic jumps with an abrupt drop

In high dam construction projects in China, stilling basin design with an abrupt bottom drop is sometimes introduced to reduce the bottom velocity and pressure loads by generating A-type hydraulic jumps. Although the stilling basin design is not new, A-type hydraulic jumps have not been studied taking into account the air entrainment and evolution of internal air–water flow structures. This paper presents an experimental study of self-aerated A-type jumps in terms of bubble transport and free-surface fluctuations over the bottom drop. Four Froude numbers from 4.1 to 10.3 are tested for three drop heights, in addition to the flat-bottom case. Compared to the classic hydraulic jumps, A-jumps are observed with longer jump lengths and weaker free-surface fluctuations. The downward deflection of the jet-shear flow and formation of a bottom roller in the step cavity require a modification to the analytical expression of velocity and void fraction distributions. The relationship between the bubble diffusivity and jump spreading rate differs from that in classic hydraulic jumps, suggesting a faster expansion of the bubble diffusion layer than the turbulent shear flow downstream of the drop, especially for large drop heights. At large approach velocities, the reattachment of the deflected jet-shear flow to the lowered bed may cause a local rise in bubble counts downstream the bottom roller. Further increase in drop height results in a W-jump with overwhelming bottom roller over the surface roller and an arced surface jet, which is beyond the scope of this study.

A Study on the Movement Characteristics of Fuel in the Fuel Tank during the Maneuvering Process

To investigate the movement characteristics of fuel within an aircraft’s fuel tank during maneuvering, this study employs numerical simulations using the Finite Pointset Method (FPM) with specific boundary conditions and excitation. The simulation results successfully capture the complex phenomena of fuel free surface fluctuations, surging, rolling, and breaking, along with the corresponding changes in the center of gravity induced by fuel movement. Throughout the aircraft’s maneuvering process, the longitudinal center of gravity experiences minimal variations, whereas the aerodynamic center of gravity exhibits significant fluctuations, reaching a range of 0.47 m. The longitudinal center of gravity consistently shifts backward with a displacement of 0.41 m. The maximum height attained by the liquid’s free surface during aircraft maneuvering measures approximately 0.22 m, reaching the upper panel’s height of the wing fuel tank, resulting in a certain level of impact on the upper panel. The maximum impact force generated during the aircraft maneuvering process amounts to 2.3 × 105 pascals, with the point of action located at the junction of the transverse frame and the upper panel. The findings of this work provide support for the safe design of aircraft fuel tank systems.

Temporal Prediction of Landslide-Generated Waves Using a Theoretical–Statistical Combined Method

For the prediction of landslide-generated waves, previous studies have developed numerous empirical equations to express the maximums of wave characteristics as functions of slide parameters upon impact. In this study, we built the temporal relationship between the wave characteristics and slide features. We gave specific insights into impulse waves generated by snow avalanches and mimicked them using a buoyant material called Carbopol whose density is close to that of water. Using the particle image velocimetry (PIV) technique, the slide’s temporal velocity field and thickness, as well as the temporal free water surface fluctuation, were determined experimentally. Using a statistical method denoted as panel data analysis, we quantified the temporal wave amplitude from the time series data of the thickness and depth-averaged velocity of the sliding mass at the shoreline. Then, the slide’s temporal thickness and velocity at the shoreline were estimated from the parameters of the stationary slide at the initial position, based on the viscoplastic theory. Combining the panel data analysis and the viscoplastic theory, the temporal wave amplitudes were estimated from the initial slide parameters. In the end, we validated the proposed theoretical–statistical combined predictive method with the support of experimental data.

Hydraulic Prototype Observation Tests on Reconstructed Energy Dissipation Facilities

In order to assess the effectiveness of reconstructed energy dissipation facilities (EDFs) in open channels at hydropower stations, hydraulic prototype observation (HPO) tests are conducted to investigate the characteristics of discharge flow and the dynamic response of hydraulic structures during sluice opening periods. While hydraulic model tests (HMTs) are commonly utilized in laboratory settings to study these characteristics, experimental conditions cannot fully replicate the real-world operations of such structures. HPO tests are employed to examine flow patterns, free water surface fluctuations, and pulsating pressure changes in open channels under varying flood discharge conditions (FDCs). Flow patterns in open channels are recorded via video; free water surface fluctuations are measured using total-station and laser rangefinder instruments; and pulsating pressure is monitored with pressure sensors and data collection systems. Flow pattern observations concentrate on addressing adverse water flow phenomena, such as turbulence, surging, and backflow. The examination of free water surface fluctuations aims to verify whether the height of the guide wall along the open channel fulfills the necessary requirements and assess the effectiveness of energy dissipation of the EDF. To comprehend the variations in pulsating pressure within the continuous sill and the base slab, nine measurement points were established across three sections perpendicular to the continuous sill’s axis on three distinct elevation levels. Additionally, three measurement points were positioned on the reinforced base slab along the open channel’s axis. The findings indicate that the impact on the continuous sill caused by discharging water is more severe when the discharge rate of a single sluice gate reaches 500 m3/s than in other FDCs. To ensure the safe operation of open channels during flood discharge, the discharge rate for each sluice gate should be reduced to 250 m3/s. The dominant pulsation induced by discharge flow falls within the low-frequency range, resulting in minimal adverse effects on the stilling basin and guide wall. The flow pattern within the stilling basin remains stable under various FDCs, with no significant adverse hydraulic phenomena observed. Parameters, including free water surface fluctuations and pulsating pressure variations, lie within acceptable ranges. These observations suggest that the arrangement of the reconstructed energy dissipation facilities is generally effective following technical reconstruction.

Gravity-driven film flow inside an inclined corrugated pipe: An experimental investigation of corrugation shape and tip width

Fluorescence images were acquired in gravity-driven film flow through inclined corrugated pipes representing a range of corrugation shapes and tip widths. The film flow developed an identifiable statically deformed free surface with a wavelength similar to the substrate for most cases of corrugation shape and tip width. The amplitude and phase shift of the statically deformed free surface, as well as the steady-state film thickness, varied more with tip width than with corrugation shape. Transient fluctuations in the free surface elevation were examined for evidence of periodic traveling waves. In general, the film flow produced transient free surface fluctuations, and in many cases, periodic traveling waves with parameters that varied similarly with corrugation shape as with tip width. For flow conditions that produced positive phase shift, low amplitude, or minimal curvature of the statically deformed free surface, transient and periodic behavior were suppressed, supporting previous findings on the importance of the shape and position of the statically deformed free surface. An increase in corrugation tip width also reduced the transient and periodic response. These two findings implicate flow dynamics in the substrate trough as a leading factor in the development of transient and periodic behavior. Steady-state response and the existence of time-dependent behavior are influenced more by tip width than corrugation shape, in agreement with two-dimensional film flow over topography; however, transient fluctuation and periodic traveling wave parameters are similarly influenced by corrugation shape and tip width, which contrasts two-dimensional findings.

Hydrodynamic response of moored ships to seismic-induced harbor oscillations

Free-surface oscillations induced by seismic waves were observed in many harbors. These free-surface fluctuations could lead to damage in a wide range of forms, such as breakage of mooring systems due to excessive ship motions. The damage to moored ships and mooring systems will remarkably reduce their emergency capability to incoming tsunamis, probably further leading to property losses and casualties. However, investigation of floating bodies under seismic-induced free-surface oscillations is rare. Particularly, the hydrodynamic response of moored ships to seismic-induced harbor oscillations has not yet been studied. In this article, the transient hydrodynamic characteristics of moored ships under seismic-induced harbor oscillations are investigated by a hybrid Boussinesq-panel model where the free-surface oscillations are modeled by a fully nonlinear Boussinesq wave model and are further used to drive the ship motions. Results reveal that seismic-induced harbor oscillations can trigger long-period movements of moored ships, consistent with the existing observations. The long-period ship motions consist of the natural modes of the mooring system and the forced modes relating to long-period harbor oscillations. Notably, the ship's maximum displacement can be amplified remarkably when the periods of natural modes coincide with those of the forced modes. The effects of modal shapes of seismic-induced multi-mode harbor oscillations on the ship motions are analyzed. Finally, a brief discussion on studying the countermeasures against ship motions triggered by seismic-induced harbor oscillations is presented. • The hydrodynamic response of moored ships to seismic-induced harbor oscillations is first investigated using a hybrid Boussinesq-panel model. • The capacity of seismic-induced harbor oscillations to trigger long-period movements of moored ships is revealed, especially reproducing a typical process of this phenomenon. • The transient hydrodynamic characteristics of moored ships under seismic-induced harbor oscillations are analyzed, especially considering the resonant case when the natural periods of the ship motions are close to that of harbor oscillations. • The effects of modal shapes of seismic-induced multi-mode harbor oscillations on the ship motions are examined.

Flow field characteristics of a two-dimensional moonpool under uniform flow conditions

ABSTRACT Moonpools are holes in the middle of a ship's hull and through its deck. In this study, the flow mechanisms in moonpools in calm water were investigated. Star-CCM+ software was used to calculate the flow within a two-dimensional (2D) moonpool under uniform flow conditions. A 2D moonpool numerical calculation model was constructed, and the convergence analysis results and experimental data were used to verify the accuracy of the calculated results. Flow field and free surface fluctuations are the main factors that cause the drag force of the moonpool. The drag force increases with the flow velocity, and the drag coefficient presents different trends at different stages. With an increase in the Froude number, Fr, the 2D moonpool enters the frequency lock-in state of the piston and sloshing natural frequency. Additionally, increasing the moonpool length results in a nonlinear change in the flow state.

Flow aeration and surface fluctuations in moderate-slope stepped chute: from aeration inception to fully developed aerated flow

ABSTRACT Although stepped chute flows have been studied for a variety of chute geometries and flow conditions, reports on air–water flow development in the fully developed aerated region are not as comprehensive as those in the nonaerated and developing aerated regions. In this paper, skimming air–water flows in a large stepped chute (1V:2.5H) were studied comparatively for two step heights, showing different stages for velocity and aeration development downstream the inception point. The mean air concentration reached a constant level while the bubble frequency kept increasing slowly in the fully developed region. The developed mean air concentration was related to the sloping angle, step height and flow discharge. The results provided possible prediction of maximum bubble frequency and its longitudinal evolution, and a glance at the scale effect on it. The free-surface fluctuations and splash height were presented, with particular attention to the effects of step height on the turbulence and aeration modification.

Ultra Low Frequency Wave Produced by Underwater Oscillating Sphere and Its Measurement

When an underwater target moves in viscous fluid, it may cause the periodic movement of the surrounding fluid and generate ultra-low-frequency (ULF) gravity waves. The initial domain of the gravitational surface wave propagating above the moving target is named circular wave. This article studies the ULF circular wave generated by underwater oscillating sphere, which will provide basis for underwater long-range target detection. Firstly, the circular wave caused by the sphere oscillation in a finite deep fluid is studied based on the theory of linear potential flow. Meanwhile, the multipole expansion theory is established to solve the circular wave field. Secondly, the interface wave generated by the target oscillation in a two-layer fluid are numerically analyzed by comparison with the free surface fluctuation of a single-layer fluid. The results show that the amplitude of the internal interface displacement (AIID) is smaller than that of the free surface (AFSD). When the sphere is in the lower layer, the layering effect of the fluid has significant influences on the AFSD. Finally, the results of the pool experiment verified that the wave generated by the oscillating sphere is the surface gravity wave. Furthermore, the change trend of the test result is consistent with the simulation result.

The effect of substrate amplitude and wavelength on gravity-driven film flow inside an inclined corrugated pipe

An experimental investigation was conducted to determine the effect of substrate amplitude and wavelength on gravity-driven film flow inside an inclined corrugated pipe. Nine different geometries were examined, with substrate amplitude and wavelength varied independently. A statically deformed free surface occurred for all conditions. The amplitude of the statically deformed free surface depended on substrate amplitude and wavelength, with phase shift unaffected by changes in substrate geometry for many conditions under investigation. Fluctuations in free surface elevation were enhanced at low substrate amplitude and intermediate substrate wavelength. Notable reductions in transient free surface behavior were observed for conditions that resulted in a positive phase shift. Transient free surface behavior developed into periodic traveling waves without applied external forcing. Frequency selection for traveling waves was strong, and traveling waves were detected for a majority of the conditions examined. The frequency, phase velocity, and wavelength of the traveling waves showed a potential dependence on substrate geometry; however, there were ranges of substrate amplitude and wavelength for which traveling wave characteristics remained unaffected by changes in substrate geometry. An examination of the amplitude of the statically deformed free surface and transient free surface fluctuations revealed that waviness is a potentially suitable method for combining the effects of substrate amplitude and wavelength on film flow in corrugated pipes. The comparison of amplitudes highlighted a possible link between the statically deformed free surface and the emergence of transient behavior and traveling waves. Length scales proposed in our original work showed promise for characterizing some results.

Numerical simulation for coastal morphodynamics using DEM-MPS method

Numerical simulations were performed for morphodynamics with free water surface fluctuation using the DEM-MPS method, which employs the discrete element method (DEM) and the enhanced moving particle semi-implicit (MPS) method for the solid and liquid phases, respectively. The reproducibility of the DEM-MPS method to a swash ripple formation process of a mixed grain bed is demonstrated. There, the bed is fully covered with water, and its void is filled with pore water. It is suggested that the ripple formation with coarse-grained particles activates the momentum exchange in the surface layer of the movable bed. In addition, a numerical simulation for a solitary wave induced by a landslide by DEM solid particles was carried out. Here, the applicability of the model in the situation where the pore water surface exists in a moving and deforming solid-sediment layer is examined. The simulation results show that it is essential to apply the apparent volume to a fluid particle inside a solid-sediment layer to predict the water surface evolution accurately.

PIV and BIV Measurements of Roller in Hydraulic Jumps

Park, M.; Kim, H.S.; Choi, S., and Ryu, Y.-U., 2021. PIV and BIV measurements of roller in hydraulic jumps. In: Lee, J.L.; Suh, K.-S.; Lee, B.; Shin, S., and Lee, J. (eds.), Crisis and Integrated Management for Coastal and Marine Safety. Journal of Coastal Research, Special Issue No. 114, pp. 56–60. Coconut Creek (Florida), ISSN 0749-0208. This study performed an experimental investigation on roller in hydraulic jump. Based on the similarity between tidal bore and hydraulic jump, the turbulence flow and free surface fluctuation of the hydraulic jump roller were analyzed with adjustment of downstream water level. To obtain instantaneous flow field including bubbly flow, PIV and BIV technique with shadowgraphy was applied. The result found that the streamwise turbulent flow was dominated at the lower part of roller while the vertical turbulence increased near the water surface of roller in hydraulic jump. The water level showed a large fluctuation as a hydraulic jump occurred. These challenges identified the detailed view of velocity and free surface of roller region can be provided using image analysis.

Experimental study of underwater pulse detonation gas jets: Bubble velocity field and time–frequency characteristics of pressure field

Underwater pulse detonation gas jets generated by a detonation tube are experimentally investigated in this study utilizing detonations in explosive gas mixtures to generate pulsating bubbles under water. Three stoichiometric gaseous fuels (methane, hydrogen, and acetylene) are detonated with oxygen under the same filling conditions. Digital particle image velocimetry and wavelet transform techniques are introduced to analyze bubble dynamics and pressure field characteristics by means of which the velocity field of the bubble interface and the time–frequency distributions of the pressure response under water are elucidated, respectively. Motions of the bubble interface, which can now be clearly seen with the oscillations, are indicated in high-speed photographic images. Three main frequency components and their duration are identified: reverberations of water tank, pulsations of the detonation gas bubble, and fluctuations of free water surface. Experimental results show that the reverberation concentrating in high frequencies is due to the detonation wave (DW) and reflected shock waves in the water tank; the pulsations are related to the bubble oscillating periods, which are stronger as the detonation pressure increases; and fluctuation occurs in both the bubble oscillating and floating stages. To explain the directional growth of the detonation gas bubble, an experiment of pulse detonation gas jet in air is conducted where the sudden release of detonation products behind the DW and the subsequent impulsive detonation gas jet are qualitatively presented. Results presented in this paper give in-depth analysis of pulse detonation gas jets and provide a new way to generate pulsating bubbles under water.